
where \(w_i^{(b)}\)  are iid with mean and variance equal to 1. Examples include Gaussian weights \(w_i^{(b)} \sim \mathcal {N}(1,1)\) , exponential \(w_i^{(b)} \sim \exp (1)\) , or Poisson \(w_i^{(b)} \sim \text{Pois}(1)\) . This is known as a multiplier, or exchangeably weighted, bootstrap.See [1]} and [2]}. The Poisson bootstrap approximates, with computational advantages, the standard \(n\)  out of \(n\)  bootstrap [3]}. Similar to resampling, the weights should vary only between clusters in clustered data, and more generally match the dependence of the data. Depending on the setting, reweighting can be preferred to resampling. For instance, if \(\theta \)  includes fixed effects, resampling can produce samples with no observation that is informative about one of the fixed effects.This is also an issue for censored models where resampling can result in datasets with no censored observations. This also affects sgd; with \(m=1\)  a gradient is only informative about at one fixed effect at a time. This makes convergence very slow, see Appendix REF  for an illustration.
